Just take a panorama using your phone's Camera app or another third-party app of your choice and send it like you'd usually send a normal photo from the app itself or from your gallery. Same goes for 720p videos, except you can also send them straight from your News Feed or from another Messenger conversation. The recipients will know they're no ordinary media by the compass icon that appears next to panoramic photos and the HD and SD marker that shows up next to high-quality videos. They can view a 360-degree image by dragging it around on the screen or by moving their phones. As for the videos, recipients can use the marker to lower their quality in full screen mode in case they want to save mobile data or if their connection's pretty bad.
You can send and receive 360-degree photos in Messenger wherever you are in the world and whether you're on iOS or Android. However, you'll only get the ability to send and receive HD videos if you're in Australia, Belgium, Canada, Denmark, Finland, France, Hong Kong, Japan, Netherlands, Norway, Romania, Singapore, South Korea, Sweden, Switzerland, Taiwan, the UK and the US.